The conference will take place at CIRM (Centre International de Rencontres Mathématiques) in Luminy Marseille, France, from August 28th to September 1st 2017.

Registration to the conferencePre-registration before June 18th 2017.
The conference are free but registration is mandatory due to limited place, accomodation and restauration is provided by CIRM with fees (see CIRM ).

TGSI2017 is dedicated to the geometrical and topological foundations of information theory. It will complement the 2017, 2016, 2015 and 2013 edition of "Geometric science of information" and "Information Geometry and its Applications IV", by focusing on the advances of entropy and information functions in probability, geometry, homology, algebra, category theory and their expression in physic and data analysis. There have been rapid recent developments in several different research communities in this connection, with little interaction between them, and one of the goals of the conference is to bring these communities in contact.
Information theory lies at the intersection and nonetheless at the foundations of several scientific disciplines, statistical and quantum physic, complex systems including biology, cognition and social systems, and by definition Information sciences and technologies ranging from computational aspects to signal and data analysis. Its industrial, social applications and impact is hardly quantifiable since the successive steps of maturation of the theory has accompanied and allowed the industrial and then the digital revolution (Nahin, P. J. The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age. Princeton University Press, 2012). As a consequence, Information theory is probably the most obvious example of "the unreasonable effectiveness of mathematics in the natural sciences" including social sciences, both in its description and its construction. If entropy was only recognised recently to "possess the sense of humour", it kept on demonstrating us its sense of surprise, as shown by the first sentence of Borel's 1913 paper on irreversibility "It may seem pointless to return to a subject about which much has been written".
In statistics, although analysis of the geometric structure of statistical manifolds (i.e., manifolds formed by some families of probability distributions) has its roots in work of Cramér, Rao and Fisher in the 1940’s, it saw much development in the 1980’s by Amari and others. On the other hand, the algebraic geometry of statistical models began to be studied more recently by Sturmfels and others. As underlined in the last INSMI report (prospective INSMI rapport du comité national du CNRS, 2014). "Since the early 2000s, the progresses in machine learning, Bayesian statistics, and model selection for example, have overwhelmed the domain. In particular, "geometric" methods have emerged, based on differential geometry and other geometries (Hessian, or Kähler or symplectic or contact...). This new family of methods are grouped under the generic term of information geometry."
In physics, the geometric aspects of information theory played a key role in the formalisation and description of quantum states and correlations that are now investigated in the context of quantum gravity. Those new developments continuously renew the traditional hope that "tomorrow, we will have learned to understand and express all of physic in the language of information" (J.A. Wheeler).
In probability theory, it is now recognized that information-theoretic inequalities play a foundational role, being closely connected to central themes including limit theorems, concentration of measure, suprema of stochastic processes, convergence rates of Markov processes to stationarity, and so on. In convex geometry, entropy is closely connected to central questions like the hyperplane conjecture. In category, homology and homotopy theory, researches have advanced on the axiomatization and characterisation of information and probability theory, and could uncover some operad or motive related structures. In geometry, thanks to work of Lott, Villani and Sturm, entropy has provided new ways of talking about curvature for spaces without a Riemannian structure, which was inconceivable before.
The conferences will review many of these new developments involving the interplay of information and algebraic and differential geometry, number theory, probability and homology. The conference will emphasize the richness and diversity of information approaches and principles that arose in mathematics, physics, and statistical data analysis (...), and will pursue at the same time the perspective of establishing a coherent theory. It emphasizes an active participation of young researchers to discuss emerging topics of collaborative research.
The conference are organised in half day and day sessions covering one central topic. Introductory courses open to students are proposed at the beginning of each session, then completed by more specialized one-hour presentation, and a session of working-discussion that tackle open questions and future development lines.

We thank Fanny Pra, Jennifer Bedigian (Inserm UMR10_72 UNIS) and Laure Stefanini, Olivia Barbaroux, all CIRM's administration for the great work and help on the administrative aspects, and all CIRM's organisation and working people for their generous and kind hosting.
We thank Guillaume Hennenfent for all the video capture and postproduction!